L2 discretization of Sturmian wave functions for Coulomb-like potentials

• Published in: International journal of quantum chemistry Vol. 107; no. 4; pp. 832 - 844
• Main Authors: Frapiccini, A. L., Gonzalez, V. Y., Randazzo, J. M., Colavecchia, F. D., Gasaneo, G.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 2007
• Subjects: Coulomb potential; Coulomb screened potential; Pollaczek polynomials; Sturmian functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.21220

In this work we introduce a method to construct Sturmian functions for general interaction potentials in two‐body problems. We expand these Sturmians on a finite L2 space, using N Laguerre basis functions to obtain a discrete set of eigenvalues for positive and negative energies. Orthogonality and closure relations are thus rewritten for these expansions; completeness is achieved through increasing the basis size. We apply the method to the Coulomb and Herman and Skillman potential. We study the behavior of the functions obtained and their convergence for an overall range of energies. The Sturmian functions are applied to solve the Schrödinger equation for an active electron in a He‐like system. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007